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arXiv · 2308.16867

Uniformizable functional Alexandroff spaces

Fatemah Ayatollah Zadeh Shirazi·Elahe Hakimi·Arezoo Hosseini·Reza Rezavand
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Abstract

In the following text we show that the Alexandroff space $X$ is uniformizable if and only if the collection of all smallest neighbourhoods is a partition of $X$. Moreover the Alexandroff space $X$ is uniformizable and functional Alexandroff ($k-$primal) if and only if the collection of all smallest neighbourhoods is a partition of $X$ into its finite subsets.

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Fatemah Ayatollah Zadeh Shirazi, Elahe Hakimi, Arezoo Hosseini, Reza Rezavand. 2023-08-31. Uniformizable functional Alexandroff spaces. https://arxiv.org/abs/2308.16867

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